The two functions x(t) and y(t) satisfy the simultaneous equations dx dy 2y dt – sint, + 2x = 5 cost. dt Find explicit expressions for x(t) and y(t), given that x(0) = 3 and y(0) = 2. Sketch the solution trajectory in the xy-plane for 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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The two functions x(t) and y(t) satisfy the simultaneous equations
dx
dy
2y
dt
– sint,
+ 2x = 5 cost.
dt
Find explicit expressions for x(t) and y(t), given that x(0) = 3 and y(0) = 2.
Sketch the solution trajectory in the xy-plane for 0 <t < 27, showing that
the trajectory crosses itself at (0, 5) and passes through the points (0, –3) and
(0, –1) in the negative x-direction
%3D
Transcribed Image Text:The two functions x(t) and y(t) satisfy the simultaneous equations dx dy 2y dt – sint, + 2x = 5 cost. dt Find explicit expressions for x(t) and y(t), given that x(0) = 3 and y(0) = 2. Sketch the solution trajectory in the xy-plane for 0 <t < 27, showing that the trajectory crosses itself at (0, 5) and passes through the points (0, –3) and (0, –1) in the negative x-direction %3D
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